Electron lens



Dec. 29, 1959 w. GLASER' 2,919,381

ELECTRON LENS Filed July 25, 1956 6 Sheets-Sheet 1' Z Ar= MoCsS oINVENTOR Walter Glaser FM JEIJ B W l yk ATTORNEYS Dec. 29, 1959 w,GLASER 2,919,381

ELECTRON LENS Filed July 25, 1956 I 6 Sheets-Sheet 2 FIG.5

FIG. 7 x

FIG. 8

INVENTOR *WolTer Glaser WM A LLM WW1J 7QL ATTORNEYS W. GLASER ELECTRONLENS Dec. 29, 1959 s Shets-Sheet 5 Filed July 25, 1956 INVEKNTOR VolrerGlaser B ATTORNEYS ELECTRON LENS 6 Sheets-s 4 Filed July 2 5. 1956INVENTOR Walter Glase BY WM M mm y f ATTORNEYS Dec. 29, 1959 w. GLASER2,919,381

ELECTRON LENS Filed July 25, 1956 e Sheets-Sheet s INVENTOR WalterGlpser ATTORNEYS Dec. 29, 1959 Filed July 25', 1956 w. GLASER 2,919,381

ELECTRON LENS 6 Sheets-Sheet 6 INVENTOR alter Glaser ATTORNEYS Fig. 16;

Patented Dec. 29, 19 59 ELECTRON LENS Walter Glaser, Mount Vernon, N.Y.,assignor to Farrand Optical Co., Inc., New York, N.Y., a corporation ofNew York Application July 25, 1956, Serial No.'600,135 v 18 Claims. (Cl.31531) This invention relates to electron lenses and particularly toelectron lenses and combinations thereof which can be corrected forspherical aberration. 1

The invention provides electron lenses having about their axes two-foldrather than complete rotational symmetry and which operate stigmaticallyin the range of Gaussian dioptrics. These lenses of the inventioncomprise two four-pole elements, either electrostatic orelectromagnetic, suitably spaced in accordance with the principles ofthe invention and rotated with respect to each other through 90 abouttheir common axis. The invention further provides electron lenses offour-fold symmetry which possess negative spherical aberration of thethird order. These lenses are employed according to the invention asprojection lenses in combination with a preceding rotationally symmetricobjective lens to provide a compound microscope corrected with respectto spherical aberration of the third order.

The invention will now be described in detail in terms of a number ofexemplary embodiments by reference to the accompanying drawings inwhich:

Fig. 1 is a diagrammatic perspective view of an electrostatic four-polelens according to the invention;

Fig. 2 is an elevational view of one of the four-pole elements of thelens of Fig. 1;

Figs. 3 to 6 are diagrams useful in explaining the invention; i

Fig. 7 is a diagrammatic perspective view of a magnetic four-pole lensaccording to the invention;

Fig.8 is an elevational view of one of the four-pole elements of Fig. 7;

Fig. 9 is a diagrammatic perspective view of a fourpole electrostaticelectron lens according to the invention including two eight-poleelements, shown in association with a rotationally symmetric objectiveelectron ing the operation of the apparatus of Fig. 9;

Fig. 12 is a diagrammatic perspective view of a fourpole magnetic.electron lens according to the invention including two eight-poleelements, shown in association with a rotationally symmetric objectiveelectron lens preceding it;

Fig. 13 is an elevational view of one of the eight-pole elements of thelens of Fig. 12;

Fig. 14 is a perspective view of one form of four-pole electrostaticelectron lens according to the invention;

Fig. 15 is a view in elevation of an eight-pole element for use with thelens of Fig. 14;

Fig. 16 is a perspective diagrammatic view of one form of magneticfour-pole electron lens according tosthe invention;

Fig. 17, is a view in elevation of one form of an eightpole magneticelement suitable for use with the lens of Figs. 18 and 19 areperspective diagrammatic views of other forms of four-pole electronlenses according to the invention; and

i Figs. 20 and 21 are diagrammatic perspective views similar to those ofFigs. 9 and 12 illustrating projection lenses according to the inventionwhich include three eight-pole elements. Rotationally symmetric electronlenses whether ofthe electrostatic or magnetic type are afliicted withspherical aberration of the so-called under-corrected type in which therays departing for example from an axial object point at higher apertureangles intersect the axis after passing through the lens at positionsnearer the lens than do rays departing at lower aperture angles. Thisstateof affairs is illustrated in Fig. 4, where there is shown afragment of a magnetic electron lens 2 operating to produce an image ofan axial object point P For paraxial rays, i.e. rays the aperture angleof which is small enough so that, for the degree of'resolution desiredin the image,

only first-order terms need be considered, the image point lies on thelens'axis at P Rays of larger aperture angle,

a for which the third-order terms must be considered, in-

tersect the axis short of P In the Gaussian image plane transverse tothe axis at P the rays passed by the lens produce a circle whose radiusAr is given by Ar=M C 8 in which M is the angular magnification at whichthe lens is operating with respect to the points P and P C is thespherical aberration constant of the lens, and 6 is the aperture anglefor the ray in question, e.g. the ray of highest aperture angle passedby the lens. If for a particular ray of aperture angle 6 the componentsof the aperture angle on two orthogonal x--z and y-z meridian planes areidentified as a and ,6 (cf; Fig. 5); the xand y-departures in theGaussian image plane at P in Fig. 4 of the intersection of that ray withthat plane will be given by The fact that'the lens is 'undercorrected isexpressed by the fact that C is positive for all rotationally symmetricelectron,

lenses, electrostatic as well as magnetic. Consequently it is notpossible to correct the spherical aberration of one such lens bycombining it with an overcorrected rotationally symmetric lens, as iscommon in' light optics.

Fig. 6 illustrates the eflect of compounding two rotationally symmetricelectron lenses 4. and 6, diagrammatically illustrated by means of theirprincipal planes. The lens 4 produces from an object point P anintermediate image whose Gaussian image plane intersects the system axisat P,,. This intermediate image is transferred by the lens 6 to a finalimage for which the Gaussian plane intersects the system axis at P A rayfrom P of aperture angle 6 larger than paraxial and having components caand B intersects the Gaussian plane at P in a point having coordinates Iin which M is the magnification at which the lens 4 operates withrespect tothe point P and C is-the spherical aberration constantthereof. The same ray on passing through the lens 6 intersects theGaussian image Consequently an image corrected for spherical aberrationof the third order will appear in the final image plane at P if t 1 MCondition cannot be satisfied with rotationally symmetric electronlenses. electron lenses which are not rotationally symmetric. Inaccordance with the invention there are provided nonrotationallysymmetric lenses of two-fold symmetry, com prising two four-poleelements, which produce stigmatic undistorted images in the first orderregion. Further in accordance with the invention there are providedlenses of four-fold symmetry, comprising two four-pole elements and twoor more eight-pole elements, which possess efiectively a negativeconstant of spherical aberration in the third order region. Further inaccordance with the invention there are provided compound lenses comprising a rotationally symmetric electron lens and a nonrotationallysymmetrical lens, the compound lens being corrected for sphericalaberration of the third order.

Fig. l is a diagrammatic perspective view of an electrostatic four-polelens according to the invention. This lens possesses two orthogonalplanesof symmetry. In the figure these are the xz and yz planesidentified by the system of coordinates shown. The lens of Fig. 1comprises two four-pole elements generally indicated at 8 and 10,suitably supported in coaxial relation by means not shown. The electronoptical axis is identified as the z-axis of a system of xy-z rectangularcoordinates. The two four-pole elements are; identical. Each com prisesfour electrostatic poles 12 equiangularly spaced about the lens axis.These are suitably supported by insulating means not shown so that anelectrostatic potential difference can be maintained in successivelyopposite polarity between circumferentially adjacent poles in eachfour-pole element. Moreover thetwo four'pole The invention provideshowever axis of each element (Fig. 2), the potential difference ubetween the oppositely charged poles thereof and the incident energy Uof the electrons upon entering the lens, it is possible to define forthe four-pole lens comprising the two four-pole elements 8 and 10 adimensionless parameter p 2 U l e U in Equation 11 e is a relativisticcorrection factor given y is the specific change ofthe electron and c isthe velocity of light.

While a lens consisting of two four-pole electrostatic elements such as8 and 10 in Fig. 1, or two four-pole magnetic elements such as 24 and 26in Fig. 7 is convergent in both of its meridian planes of symmetry andhas the same power in both, the principal-planes with respect to the twosymmetry planes are in general at different axial locations so that thefocal points will not coineide and the system will be astigmatic. Inaccordance with the invention however stigmatic images, are produced bya proper spacing of the two elements.

The lens of Fig. 1 will produce stigmatic undistorted images of thefirst order when the two four-pole elements are separated by a spacing 0between the axial mid planes of the four-pole elements which is relatedto the element thickness d and the lens parameter [c by the relation:

focal points i andf of the lens comprising elements 8 and 10 are distantfrom the lens center plane, i.e. the plane perpendicular to the lensaxis andhalf way between elements 8 and 10, by distances Z and Zgivenby:

real/a r elements are displaced 90 with respect to each other about thesystem axis so thatin Fig. 1 in the element 8 the poles centered on thex-z plane are positive while in the element 10 the elements centered onthe xz plane are negative. The lens is shown in association with anelectron source including a cathode 16 and accelerating electrode 18, asource of accelerating voltage 20 and a source of lens voltage 2.2. Fig.2 shows the appearance of the elementsS and 10 in elevation, togetherwith the shape of the field between the poles thereof.

In the xz plane the element 8 is evidently divergent on a beam ofelectrons passing down the system axis whereas it is convergent in. they-z plane, and vice versa in the case of the element 10. Together thetwo fourpole elements of thelens of 'Fig. 1 have anet'convergent eifectin each of the orthogonal planes of symmetry of the lens. In terms ofthe axial thickness d of each 'of the four-pole elements, the radius ofthe opening on the The focal lengths of the lens of Fig. 1, not shown toscale in Fig. 3, are such that'object locations which will result in theformation of an enlarged image lie within the field produced by thefirst four-pole element. For thisreaso'n the lens is used as aprojector, and provides image formation by operation on thc asymptotesof the rays from a preceding objective lens from which it is so spacedthat, assuming the lens of Fig. 1 for the moment de-energized, theintermediate image produced by the objective will lie outside the firstprincipal focus Z of the lens of Fig. 1. When the lens of Fig. 1 is thusenergized, it will produce a final image which is stigmatic andundistorted to the first order, if the virtual object employed therewithisv similarly, stigmatic and undistorted.

Fig. 7 is a diagram similar to that of Fig. 1 but illustrating amagnetic four-pole lens according to the invention. ;The lens con1prisestwo identical magnetic four pole elements 24 and 26 which are, as inthe'case of Fig.

. 1, 90 displaced with each other rotationally about the system axis, sothat the north poles of the element 24 are aligned with the south poles'of the element 26. Each of the four-pole elements includes fourmagnetic poles 28 equiangularly displaced about the system axis asindicated in Fig. 8. Conveniently all four poles are formed on a commonyoke structure 30. The poles are energized to successively oppositemagnetic potentials by four windings 32 each generating a flux NI. Theaxial length of the four-pole elements is again denoted d, and theseparation of the center planes of the elements is c. As indicated inFig. 8 the radius of the opening between their poles is p It will beobserved that the x--z and yz symmetry planes of maximum action onelectrons'bisect the angular spacings between the magnetic poles whereasin the embodiment of Fig. 1 they bisect the electrostatic polesthemselves.

form

Here n is the inductivity of the vacuum while U and e have the samesignificance as in Equation 11. The spacing condition of the twofour-pole elements for stigmatic and undistorted Gaussian imageformation is again equation 12. For the lens of Fig. 7 the distances Zand Zp of the focal points from the center plane of the lens and thefocal lengths from the principal planes are given by the same relations(13) and (14) as in the case of the lens of Fig. 1, the lens parameter khaving however for the lens of Fig. 7 the value given by Equation 16rather than that of Equation 11. v

While the lenses of Figs. 1 and 7 have utility in forming stigmaticdistortionless first-order images, the invention further providesrotationally non-symmetric lenses which permit correction of third-orderspherical aberra tion when used with a rotationally symmetric lens asobjective. Moreover with such combinations useful magnifications may beachieved.

. In order to achieve image formation stigmatic and corrected to thethird orderit is necessary to supplement the field of two fold symmetryproduced by lenses of the type illustrated in' Figs. 1 and 7 with afield of four-fold symmetry. Figs. and 13 are elevational viewsrespective ly of eelctrostatic and magnetic eight-pole elements whichmay be employed as correctors with lenses of the form of Figs. 1 and 7in order to permit third order correction. The correcting element ofFig. 10 comprises eight electrostatic poles 34 equiangularly disposedabout an axis and charged to successively opposite electrostaticpotentials by any suitable means. Fig. l3-shows that the magnetic analogcomprises eight magnetic poles 36 equiangularly disposed about an axisand charged to successively op posite magnetic potentials. For thispurpose there are desirably provided eight windings which may eitherembrace the salient poles themselves or the portions of the externalyoke between adjacent poles. In the latter case the flux of each coil iseifective across the gap between the adjacent poles. the salient polesthemselves (as may also be done with For the lensof Fig. 7 the lensparameter It takes the When the windings are provided on the magneticfour-pole elements) the flux of each wind; ing is shared between two'pairs-of'poles having a common pole but'the resultant flux is the samein the central opening of the element.

Fig. 9 is a diagrammatic perspectiveview of an. electrostatic electronlens according to the invention comprising two four-pole elements 40 and42and two eightpoleqelements '44 and 46. Elements 40;and 42 are of 5 thetypeidescribed' in connection with Fig. 1 and are displaced with respectto each other aboutthe lens axis z.- -The spacing of the elements 40 and42 satisfy- Equation 12. In association with this lens thereis shown arotationally symmetric objective lens 48 andalso a condenserlens' 50 andan electron gun including a cathode 52 and an anode 54.

The operation of the lens of Fig. 9 can be understood qualitatively'byreference to Fig. 11 which is an electron ray 1 diagram illustratingalternatively the operation of theapparatus of Fig.'9-or of'Fig. 12. InFig. 11 an Electrons diverging from the object point P are imagedby theobjective 48. In the absence of the corrected four-pole lens comprisingelements 40, 42', 44 and '46 these electrons would be brought to focus,with spherical aberration of the third order, at an intermediate imagelocation for which the Gaussian image plane is indicated atP This imageformation is rotationally symmetric. If now the non-rotational lenscomprising elements 40, 42, 44' and 46 issuitably energized, theoperation of element 40 in the x-z plane will be divergent as indicatedby the sample pair of full line electron trajectories identified as'x(z). These may be considered either as electron trajectories in thex--z plane, or'as the projection onto that plane of trajectories outsideit. By virtue of this divergent action the trajectories x(z) come to anintermediate focus'at point P beyond Pg. Diverging from P thetrajectories x(z) are then subjected to the action ofelement 42, whichis convergent'in the Conversely in the 'yz plane the element 40 willoperate convergently, producing a pair of sample dashed line electrontrajectories y(z) which are brought to a focus at P in advance of therotationally symmetric intermediate image position P trajectories y(z)are still under the influence of element 40 and are hence made once moreconvergent. As they pass into the field of influence of element 42 how-'ever they suifer a divergent effect, so that they do not again come toa focus until they reach the axial position of P The axial position Pidentifies the position of the circle of least confusion between theastigmatic formation by means of the objective 48 and the four-,

pole elements 40 and 42 is subject to a-third order spherical aberrationcomponent which cannot in general be made equal to zero because thethird order spherical aberration contribution of the four-pole lenscomprising elements 40 and 42 alone cannot in general be made equal andopposite to the contribution of the, objective 48. According to theinvention however two or more eight-pole correcting elements such as theelemerits 44 and 46 are provided which are effective to modify theextra-axial field. With the help of x.z plane, and are hence caused toconverge again at Diverging from Py lens." s the projection lensicomprisingelements :40; 42, 44 and 46 is' identified at a bracketbythechar- I acter 41, and in Fig. 12 theprojectionlenscomprising elements.56; 58; 6tland 62 is similarly identified at a bracketby the reference.character 57. These projection I lenses of the invention, and theoperationtherein of the eight-pole elements 44, 46 and 6t), 62 will nowbe con eight-pole correcting elements the third order sphericalaberration of the complete combinationof rotationally symmetricobjective and orthogonally symmetrical projection lenses is made tovanish, without disturbing the. Gaussian image formation.

Advantageously the axial position of the first eight- With this choiceof locaelement ,46 can sufiice to provide the desired total correctionfor the objective and projection lenses, and this elementpmay be locatedbe'yo'nd the second ifour pole element 42.

Fig. 12 illustrates a magnetic lens according to'the invention analogousto the electrostatic lens of Fig. 9;

The lens of Fig, 12 includes two identical four-pole magnetic elements56 and 58 of the type described in other by 90 about a common. axis, andtwo eight-pole elements 60 and 62. ,Thcse four elements are shown inconjunction with an objective lens 640i? rotationally and sphericalaberration coefi'icient of the objective, while x, and y M is themagnification of the. projector. given by Equations4 and 3, arethecomponentsof spherical aberration produced by theobjective. v I

The axial object point P is therefore imaged axial point P to the thirdorder if into an shaped according'to the invention by suitable use ofeight-pole elementstoresultin satisfaction of the correcconnection? withFig. 7,; displaced with'respect to, each I symmetric type and with acondenser lens .66, cathode 68 and anode 70.

The operation of the lens of Fig; l2 is qualitatively explainable-withreference to Fig. 11 in the same'fa'shion as that used above withrespect to the electrostatic lens of .Fig, 9. In the case of Fig.'l2also the eight-pole corrector element 60-is located at or near theaxial posi-- v I I I ZglS the z-coorclinate of the object point P fortheobtion of the circle of least confusion in the'astigmatic bundleproduced by element 56, land element 62 is located on the side sideredin somewhat greater detail in terms of an analy' sis of the behavior ofsuch a four-element lensincomorder spherical aberration is determined bythree co-- efficients a, -b, c which appear in the contributions Ax and?A of that lens to the total spherical aberra tion in the final imageplane of the combination ofthat lens with an objective. Thesecontributions have the following form:

y1 p( a d a where again oc and B are the components of the electrontrajectory considered at the intermediate image plane P (Fig. 6) and Mis the magnification of the projection lens with respect to a virtualobject at P The total spherical aberration produced in the final imageplane at P by the rotationally symmetric objective and four-foldsymmetric projection lenses may then with the helpof theHelmholtz-Lagrange relation (7') be written madeup of x and y componentsas follows:

In Equation 18 M and C are again the magnification ofelement 58 oppositethe objective b L wer ca (00) in which x(z) and 3 (2) are two electrontrajectories satistying the inii alconditions: 1

jective. and 2, is the :z-coordinate of the final image point P a a a inEquation 20 are the spherical aberration coefficients. of the four-polelens comprising two four I pole elements only, i.e. the elements 40 and42 in Fig. 9

on 56 and 58 in Fig. 12. T hese coefiicients a 12,1613 can be calculatedforany four-pole lens according to the in- I vention, for example asillustrated in Figs. 1 and7, and 'forthe four-pole lenses included inthe four-pole eight- -,pole-lenses 41 and 57 ofFigs; 9and12. Applying(20) to- ('19). the correction conditions beweydz al M04080, fmzyywdpazwr e...

L y( s+ o w To satisfy (21) it is advantageous to put 1/ in the form:1X1+ 2X2+ 3Xa dividing 1/ into three parts which it is convenient toassociate with separate parts of the region along the axis from z to zin which separate eight-pole elements are active. In (22), C C and Cdetermine the power to be given to each of the eight-pole elements, ofwhich in general case three are required. For an eight-pole element,electrostatic or electromagnetic, the power C is specified in terms ofthe aperture p and by the voltage v or ampere turn NI between adjacentpoles by the rela- N l k 1 [Pkst) l in which y is the z-coordinate ofthe center planeof the eight-pole element in question.

The coefficientsa, I and care determined inpartby the image-formingfield of two-fold symmetry in, the paraxial region contributed .bythetwo four-pole ele- I mcntsand in part by the extra-axial field which isto be Letthis extra-axial field be determinedby an arbitrary function11/. I t

To achieve satisfaction .of the correction conditions (19) one canimpose on p the conditions:

' 9 Splitting up the integrals of (20) according to (22), one may forbrevity write:

Introducing (22) into (21) one then obtains a system of linearequations:

From this system of equations generally for any three arbitraryfunctions X2 and X3 the constants C1, C and C may be determined. In thecases illustrated in Figs. 9 and 12, X2 and X3 are so chosen that X1differs from zero only in the region in advance of the fourpole lenscomprising two' four-pole elements while X2 differs from zero onlyinside the four-pole lens and X3 differs from. zero only after or behindit, i.e. on the side of the four-pole lens remote from the objective.Since at axial positions preceding and succeeding the corrected lenses41 and 57 the system must be rotationally symmetric if stigmatic imagesare to be formed, one has with these assumed axial values for x2 and X3the relations:

may be designated 1::

"Fatwa-@ 1 Thus, the field function j H u I gc rxr+ zxz+ xs p can berealized by the use, in the 'general case, of threeeight pole elementsof the types illustrated in Figs. V10

and 13, whose strength C (in terms of interpole voltage or magneticpotential) and position X (for which z=) are given by Equations 23 and24. V

For the corrector to lie between the four-pole elements we insert X2from (33) into (32) which gives:

11 o'er-yer) oer-mew) is [pine-err Equation 34 is the condition'whichthe position of the eight-pole corrector must satisfy. 7

As is apparent from inspection of (33), X2 is a bellshaped function witha'steep maximum at z= The value of Q can be obtained by evaluation of(34). Approximately however because of this steep maximum the variable zin the numerator functionsvcan be set equal to Q, and these functionscan be taken outside the integral, in view of the negligiblecontribution of the product of numerator functions with x (z) (forvalues of X2 when z is different from 9. Since it is known that Hencethe axial position for which x2 is a maximum,

and which is the position of the center plane of the correcting element,is that at which the electron trajectory is equidistant from the x-z andy-z meridian planes, i.e. the position of the circle of least confusionin the astigmatic bundle into which the bundle from the objective istransformed by the first four-pole element.

The corresponding power C from (29) is In (37) Q in the right-handmember possesses the value required by (35). From (28) and (36) one canwrite:

r m-l- 3 as= The right-hand member of (38) is a number which can becalculated.

Equation 38 can be satisfied by setting C equal to zero, i.e. bylimiting oneself to one eight-pole Corrector element in the field-freespace outside the four-pole lens, in accordance with the examples'of theinvention illustrated in Figs. 9 and 12. In that case, the firstcorrector providing the function (3 of (22) is suppressed and the thirdcor-rector for the function C remains to be determined. Its axialposition may be arbitrarily selected to the right of the secondfour-pole element, i.e. between the second four-pole element and P1. theselection of a position therefor, for the element 46 or 62 in Fig. 9 orFig. 1-2, the value of is determined and hence X3 is determined by therelation:

1 39) X3 lP3 -l-( -a) l an appropriate choicebeing made for p Thisdetermination of X3 permits evaluation of 1 from the expression thereforin (25). With evaluation of 11 the value of C is specified by (38), andthe voltage or mag- With netic potential to be applied'to the eight-poleelement 46 or 62; according to the electrostatic orunagnetic naturethereof, may be inferred from therelation:

; analogousmo (23);. The four-element lens of Fig. :9

,or Fig. 12 is thus. completely determined,

. It is to be understood however; that theinvention is not limited tothe embodiments of Figs. 9 and 12 g in which (3 :0. Various practicalconsiderations, for

78. The two four-pole elements are'preferably identical.

76 adjusting screws :84 threaded into the casing member 72 anddiametrically-opposite =compression springs 86 positioned between thecylinder 82 and easing member symmetry axis of the element '78.

giacent ends the casing members 72 and 74 carry threads example thosepertaining to voltages necessary to be applied, may make it desirable touse three eightrpole corrector elements. These may be used consistentlywith the positioningofthe central or second one at the posi-' tion of:the circle of least confusion associated, with the first four-poleelementpnrsuant tothe assumptions made in the foregoing analysis that g-e0 only before, n -0 onlyinside, and x Oonly after the fouepole lens orSuch. lenses including two. four-pole-and three eight-poleelernentsarediagrammatically illustrated i for electrostatic andmagnetic embodimentsrespectively in Figs. and 21.

otherwise.

comprises a pair oftour pole, elements 49 and 42 com stituting togetherafour-pole lens of the type illustrated a in Fig.1 and three eight poleelements 43, 45and 47.; Elements 43, :45 and47. may be of the typeillustrated in Fig. 10. i FhE eight-pole element 43 is axially posi qtioned on the object side of the four-polelens. The ele ment 45 ispositioned between the two element of the: i

The electrostatic lens of Fig. 20. ,i

four-pole lens, and the element 47 ispositioned on the image side of thefour-pole lens; ;The magnetic lens of Fig; 2:1 comprisesa; pair offour-pole elements 56' and 58 constituting togetherafouepole lens ofthetypeiillus- I trated in Fig. 7 and three eightpole el ements59, (i1.and -63. Elements-59;, 61 and63 may be of the type illus- :trated in,Fig. l3 i The eight-pole element 59: is axially positioned on the objectside of the four-pole lens. The

element 61 is positioned between the two elements of the t four-polelens, andthe element 63:,is positionedon the image side of the'four-polelens. It is' also for example possible to employ two eight-polecorrecting elements within the four-pole field. If two rather than threecorrecting elements are to be employed, it is of course also possible toprovide one between P and the fourpole lens, by setting C instead of Cequal to zero in (38).

In the most general sense, the invention contemplates the use of threeeight-pole corrector elements in any combination of axial positionswhich permit satisfaction of Equations 26. From these equationsgenerally, for any three arbitrary functions X3 the constants C C and Ccan be determined, With eight-pole elements the functions x, describingthe axial dependence of the fields, produced by those elements, willhave the form of Equation 24 while the strengt thereof will bedeterminedby relations of the form of Equation 23.

The poles in the electrostatic elements of the figures thus fardiscussed have been shown as having the shape of short hyperboliccylinders. This shape for the poles is a theoretically desirable onewhich may be applied to the poles of magnetic elements as well as tothose of electrostatic elements. The improvement achieved by thehyperbolic cylindrical shape for the poles is however primarily in theextra-axial region where the field is under primary control of theeight-pole correcting elemcnts. Lenses according to the inventiontherefore need not be constructed with a hyperbolic cylindrical shapefor the poles.

Constructional forms for four-pole lenses according to the invention areshown in Figs. 14, 16, 18 and 19, while constructional forms for eight"pole elements are shown in Figs. 15 and 17. In Fig. 14 two casingmembers 72 and 74 (shown broken away) each support one of. two four-poleelements generally indicated at 76and permit both translation androtation of the element so that its axis of symmetry can be made tocoincide with the At their adof opposite hand so that by rotation of athreaded sleeve 38 it ispo-ssible to adjust the axial spacing of thecasing membcrs and. hence of the four-pole elements76 and 73. Suitableexternal support members not showrumay be provided for the casingmembers 72and74;

By means of one or .more suitable voltage sources the poles $9 of eachfourpole element are charged with respect to each otherto asuitableelectrostatic potential, the potential difference of this source beingapplied in p i successively opposite polarities between adjacent poles80? around the system axis. The four poles 80in each elevmentare spacedsuccessively apart about the system axis, and-the connections to thesource orsourcesof po 7 tentiali are such; that the meridian of thepositively charged poles in the element 76 is themeridian ofthe:negatively charged poles in the element-78. Mech anicaL ly therefore thefour-pole elements 76. and 78 .areidentical in their orientation withrespect to the system axis; electrically however. the element7tlis-rotated-90i about that axis. from the position of the element '76.

.An' eighnpole element suitable for use withqthefour pole lens of Fig.14 is: showniinfig. {15.

an insulating ring 89 supporting eight electrostatic poles: 90 similarto the poles 80 of Fig. 14, though -advantageously of shorter axiallength. The poles -90are-equi angularly' and equidistantly disposed froman axis. The 1 structure may be dimensionedto fit insidethezsleeves :72

' l 5 Fig. 16' represents a four pole lens according to the inventionsimilar to that of Fig. 1 but electromagnetic from which there projectradially inward at 90 intervals four poles 101. Each of the poles 101forms the core for a winding 110, shown broken away. in Fig. 16, and thedirection of current flow through these windings, as indicated by dotsand crosses in the figure, is so established that in each of the twofour-pole elements adjacentpoles constitute magnetic poles of oppositesign whereas diametrically opposite poles constitute magnetic poles ofthe same sign. The currents and windings are so adjusted thatall fourmagnetic. poles of each element are of equal intensity. As with theelectrostatic embodiment of Fig. 14 the meridian occupied in element 96by the poles of one polarity is occupied in the element 98 by magneticpoles of the opposite polarity. The poles may be so shaped as topossess, in the portions thereof close to the axis, the shape ofhyperbolic cylinders.

A magnetic eight-pole element is shown in elevation in Fig. 17. Itincludes a yoke 112 from. which there project eight similar poles 114,equiangularly and equidistantly spaced from the axis. The energizingcoils 116 are shown wound about the yoke between adjacent poles.

Other constructions may be employed to produce a plurality of magneticpoles of successively opposite polarity about an axis. One suchalternate form of magnetic four-pole lens according. to the invention is'diagrammatically illustrated in Fig. 18; Here four horseshoe Itcomprises i i form angular intervals about an axis to provide two arraysof four magnetic poles alternating in polarity about the system axis,with opposite polarities in the two arrays in any given meridian. Inplace of the permanent magnets 120, electromagnets may be used instead.

Fig. 19 indicates how the desired magnetic fields for a pair of fourpole elements according to the invention may be produced simply by meansof electric currents. Eight straight conductors 124 of the same lengthare disposed in two groups of four each, all supported by means notshown parallel to and equally spaced from a system axis zz, theconductors of each group being equiangularly disposed about andequidistant from the axis. In each group the four conductors are alignedin their position lengthwise of the axis. The conductors 124 of Fig. 19are interconnected by means of radial portions 126 and remotecircumferential portions 128, and by means of a lead 130 between the.two groups of conductors. In the vicinity of the system axis and withinthe two regions defined by the two groups of conductors 124, themagnetic field is due substantially exclusively to the current flowingin the conductors 124. All eight are connected in series, and theconnection is such as to provide opposite directions of current flow incircumferentially adjacent conductors of each goup. Moreover while theconductors in a the two groups lie in a single pair of perpendicularmeridians about the axis; the interconnection of the two groups is suchthat in each meridian the direction of current flow is opposite forsimilarly positioned wires in the two groups.

Of course pairs of eight-pole elements can be built up from permanent orelectromagnets in the fashion generally indicated in Fig. 18 by doublingthe number of magnets employed, and eight-pole elements may be built upeither singly or in pairs in the fashion generally indicated in Fig. 19by doubling the number of conductors employed.

While the invention has been described in terms of a number of preferredembodiments, the invention itself is not limited to these. For exampleit is possible although not necessarily advantageous to use magneticeight-pole elements with electrostatic four-pole elements and viceversa. The two four-pole elements or four-pole sets must however be thesame. Thus they mustbe either electrostatic or electromagnetic andshould moreover be substantially identical in electron optical respects,i.e. in their influence on a beam of electrons passing through them.Both four-pole sets should include four poles spaced equiangularly aboutand equidistant from the axis with the spacing of the poles from theaxis the same for both four-pole sets. In the case of the eight-poleelements or eight-pole sets while all eight poles of any one element orset should be spaced equiangularly about and equidistant from the axisthe spacing from the axis of the poles of the separate eight-poleelements may be unlike;

. While the invention has been described in terms of the focusing ofelectrons, it is applicable to the focusing of an image formation withcharged particles of other kinds, and the claims are to be sounderstood.

I claim:

, 1. An electron lens adapted to produce an image of a virtual objectwith negative third order spherical aberration comprising two identicalsets of four poles coaxial in a common axis with the poles of said setscentered on two perpendicular meridian planes containing said axis, anda plurality of eight-pole elements coaxial in said axis. 2. An electronlens adapted for use as a projection lens in combination with anobjective, said lens comprising two sets of four poles each, the polesof both of said sets being coaxial in and equiangularly spaced about acommon axis at a common distance therefrom, the poles of both of saidsets being centered on two perpendicular meridian planes containing saidaxis, said lens further comprising a plurality of sets of eight poleseach, the poles of each of said eight-pole sets being coaxial in of saideight-pole sets being coaxial in and equiangularly spaced about saidaxis at a common distance therefrom, one of said eight-pole sets beingaxially'disposed between said two four-pole sets adjacent the circle ofleast con-- fusion in the astigmatic ray bundle produced by one of saidfour-pole sets and the other of said eight-pole sets being disposed onthe side of one of said four-pole setsremote from the other of saidfour-pole setsj 4. A compound electron lens corrected for sphericalaberration of the third order, said lens comprising a rotationallysymmetric objective lens and a projection lens of four-fold symmetrypositioned coaxially with the axis of said objective lens in position tomagnify the virtual object provided by an image of a real object formedby saidobjective, said projection lens including two sets of four poleseach, the poles of both of said sets being coaxial in and equiangularlyspaced about said axis at a common distance therefrom, the poles of bothof said sets being centered on two perpendicular meridian planescontaining said axis, said projection lens further including a pluralityof sets of eight poles each, the poles of each of said eight-pole setsbeing coaxial in and equiangularly spaced about said axis at a commondistance therefrom.

5. A compound electron lens corrected for spherical aberration of thethird order, said lens-comprising a rotationally symmetric objectivelens and a projection lens of four-fold symmetry positioned coaxiallywith the axis of said objective lens in position to magnify the virtual,

object provided by an image of a real object formed by said objective,said projection lens including two sets of four poles each, the poles ofboth of said sets being coaxial in and equiangularly spaced about saidaxis at a common distance therefrom, the poles of both of said setsbeing centered on two perpendicular meridian planes containing saidaxis, said projection lens further including two sets of eight poleseach, the poles of each of said eight-pole sets being coaxial in andequiangularly spaced about said axis at a common distance therefrom, oneof said eight-pole sets being axially disposed between said twofour-pole sets adjacent the circle of least confusion in the astigmaticray bundle produced by the one of said four-pole sets adjacent saidobjective lens and the other of said eight-pole sets being disposed onthe side of the other of said four-pole sets remote from said objectivelens.

6. An electron lens comprising two sets of four poles coaxial in acommon axis with the poles of said sets centered on two perpendicularmeridian planes containing said axis, the poles of each set beingcentered'on a plane perpendicular to said axis, circumferentiallyadjacent poles of each set being of successively opposite sign and thepoles of one set being of sign opposite to the poles of the other set atthe same positions circumferentially of said axis.

7. A lens according to claim 6 adapted to focus electrons of energy U inwhich the poles of said two sets of four poles are equiangularly spacedabout said common axis at a common distance therefrom, circumferentiallyadjacent poles ofboth-sets beingcharged in successively oppositepolarities to one of the potential dilferences u,

volts and NI ampere turns, the poles centered, on com mon half planes ofsaid meridian planes being oppositely charged, said poles having anaxial length d and a spacing between the center planes of the two setsthereof specified by in which 1+2eU+ e NI 1 p 2U l+eU W 27110 U(1+EU)wherein is the specific charge of the electron, e is one-half thespecific charge of the electron divided by the square of the velocity oflight, p is the distance of said poles from said axisand ,u is theinductivity of a vacuum.

8. An electrostatic lens according to claim 6 adapted to focus electronsof energy U in which the poles of said four-pole sets are electrostaticand are equiangallarly spaced about said common axis at a distance petherewherein is the specific charge of the electrons, e is one-half thespecific charge of the electron divided by the square of the velocity oflight, and, it is the inductivity of the vacuum, the quantities C beingsolutions of the system of equations from, circumferentially adjacentpoles of both sets being in which equations the limits ofintegrationtare the axial charged in successively opposite polarities toan electrostatic potential diiference of u volts, the poles centered oncommon half planes of said meridian planes being oppositelycharged, saidpoles havingan axial length d and a spacing c between the center planesof the two sets thereof specified by in which e is one-half the specificcharge of the electron divided by the square of the velocity of light.

9.'An electromagnetic lens according to claim 6 adapted to focuselectrons of energy U in which the poles of said four-pole sets areelectromagnetic and are equiangularly spaced about said common axis at adistance p therefrom, circumferentially adjacent poles of both setsbeing charged in successively opposite polarities to a magneticpotential difference NI ampere turns, the poles centered on common halfplanes of said meridian planes being oppositely charged, said poleshaving an axial length d and a spacing c between the center planes ofthe two sets thereof specified by wherein 2 0 e 1 N I k 5Z \/U(1+EU inwhich n is the inductivity of the vacuum is the specific charge of theelectron and e is one-half the specific charge of the electron dividedby the square of the velocity of light.

10. An electron lens according to claim 7 adapted for use in the systemincluding an undercorrected rotationally symmetric objective lens of,third order spherical aberration ooefiicient C and magnification Moperating on electrons of energy U, said projection lens comprisingposition z of the object for the rotationally symmetric lens and theaxial position 2 of the image produced by the projection lens, X2 and X3are functions of z of the form lPk-l"( x(z) and y(z) are the projectionsonto said meridian planes of an electron trajectory with the initialconditions s) Z/'( 0)= 1 and a a and a are the coefficients of thirdorder spherical aberration of the lens of claim7.

ll. An electrostaticelectron lens according to claim 6 including twosubstantially cylindrical casing members, means to support saidmembersin coaxial relation and to vary the spacing thereof, aninsulating cylinder within each of said casing members, the poles ofeach ofsaid sets being supported in mutually insulated relation within aseparate one of said cylinders, the poles in each of said cylindersbeing further centered on a plane perpendicular to said axis,rand meansto adjust one of said cylinders within its casing member to render saidaxes collinear.

12. An electromagnetic electron lens according to claim 6 in which saidpoles are magnetic, said lens comprising two substantially cylindricalcasing members, means to support said members in coaxial relation and toadjust the spacing thereof an annular magnetic yoke supported withineach of said members, the magnetic poles of each of said sets projectingradially inwardly from a separate one of said yokes, a winding embracingeach of said poles, and means to adjust one of said yokes within itscasing member to render said axes col-linear.

13. An electron lens according to claim 6 in which said two sets of fourpoles are formed by four magnets ofhorseshoe type, saidmagnets havingsubstantially identical equally spaced poles, said magnets beingdisposed with the axes of their poles parallel to and arrangedequiangularly about and equidistant from an axis, said lastnamed polesbeing centered on two planes perpendicular to said last-named axis.circumferentially adjacent poles in each of said planes being ofopposite sign.

17 14. An electron lens according to. claim 6 in which said two sets offour poles are formed by four electromagnets of horseshoe type, saidmagnets having substantially identical equally spaced poles, saidmagnets being disposed with the axes of their poles parallel to andarranged equiangularly about and equidistant from an axis, saidlast-named poles being centered on two 7 planes perpendicular to saidlast-named axis, circumferentially adjacent poles in each of said planesbeing of opposite sign.

15. An electron lens according to claim 6 in which said two sets of fourpoles are fomled by four permanent magnets of horseshoe type, saidmagnets having substantially identical equally spaced poles, saidmagnets being disposed with. the axes of their poles parallel to andarranged equiangularly about and equidistant from an axis, said lastnamed poles being centered on two planes perpendicular to saidlast-named axis, ciroumferentially adjacent poles in each of said planesbeing of opposite sign.

16. An electron lens according to claim- 6 in which said two sets offour poles are formed by two groups of four conductors each, all of saidconductors having substantially the same length, said conductors beingdisposed equiangularly about and equidistant from a common axis, saidconductors lying substantially in two perpendicular planes containingsaid axis, the conductors of each of said groups being centered on aplane perpendicular to said axis, and means to energize all of saidconductors with substantially the same current, the direction' ofcurrent flow being opposite in circumferentially adjacent conductors ofeach of said groups and opposite in aligned ones of said conductors.

17. An electron lens according to claim 6 in which said two sets of fourpoles are formed by two groups of four conductors each, all of saidconductors having substantially the same length, said conductors beingdisposed equiangularly about and equidistant from a common axis, saidconductors lying substantially in two perpendicular planes containingsaid axis, the conductors of each of said groups being centered on aplane perpendicular to said axis, all of said conductors being connectedin series for opposite directions of current flow in circumferentiallyadjacent conductors of each of said groups and for opposite directionsof current flow in aligned ones of said conductors.

' 18. An eight-pole corrector element adapted to develop a field offour-fold symmetry comprising eight substantially identical polesdisposed equiangularly about, and equidistant from an axis, and means tocharge said poles to successively opposite potentials.

References Cited in the file of this patent UNITED STATES PATENTS2,157,182 Mulofi May 9, 1939 2,200,039 Nicoll May 7, 1940 2,244,748Walker June 10, 1941 2,455,676 Hillier Dec. 7, 1948 2,472,727 SalingerJune 7, 1949 2,503,173 Reisner Apr. 4, 1950 2,513,221 Webb June 27, 19502,520,813 Rudenberg Aug. 29, 1950 2,722,621 Schenau Nov. 1, 19552,761,991 Eisfeldt Sept. 4, 1956 2,802,111 Reisner Aug. 6, 19572,802,138 Tompkins Aug. 6, 1957 UNITED STATES PATENT OFFICE Certificateof Correction Patent No. 2,919,381 December 1959 Walter Glaser K It ishereby certified that error appears in the printed specification of theabout?"- numbered patent requiring correction and that the said LettersPatent d ould read as corrected below.

Column 3, lines 20 and 21, Equation (-10) should appear as shown belowinstead of as in the patent:

column 4, lines 44 and 45, the left-hand portion of Equation (13) shouldappear as shown below instead of as in the patent:

same column 4, line 48, in the denominator of the long fraction, theparentheses should be closed after 1, first occurrence; column 5, line33, in the denominator of the fraction under the first radical sign onthe left-hand side of the Equation (16), the italicized 0 should be asubscript to the italicized m; lines 36 and 37, the fraction shouldappear as shown below instead of as in the patent:

. a column 9, lines 6 to 8, for that portion of the equation followingdz, strike out same column 9, line 73, for that portion of the equationreading read column 10, line 45, the parentheses in the denominator ofthe integrand on the righthand side of Equation (37 should appear asshown below instead of as in the patent:

-6:) same column 10, line 51, the quantity in parentheses in thenumerator of the righthand side of Equation (38) should appear as shownbelow instead of as in the patent: /3 12' 22) column 15, line 72, forthe system read a system--; column 16, lines 14 to 16, the fractionshould appear as shown below instead of as in the patent:

1. o Signed and sealed this 5th day of July 1960.

[SEAL] Attest:

KARL 11. AKLINE, ROBERT C. WATSON, Attesting Ofioer. Oommz'ssz'oner ofPatents.

UNITED STATES PATENT OFFICE Certificate of Correction Patent No.2,919,381 mber 29, 1959 Walter Glaser It is hereby certified that errorappears in the printed specification of the above' numbered patentrequiring correction and that the said Letters Patent should read ascorrected below.

Column 3, lines 20 and 21, Equation (10) should appear as shown belowinstead of as in the patent: j

column 4, lines 44 and 45, the left-hand portion of Equation (13) shouldappear as shown below instead of as in the patent:

same column 4, line 48, in the denominator of the long fraction, theparentheses should be closed after 1, first occurrence; column 5, line33, in the denominator of the fraction under the first radical sign onthe left-hand side of the Equatlon (16), the 1ta11- cized 0 should be asubscript to the italicized m; lines 36 and 37, the fraction shouldappear as shown below instead of as in the patent:

column 9, lines 6 to 8, for that portion of the equation following dz,strike out same column 9, line 73, for that portion of the equationreading read column 10, line 45, the parentheses in the denominator ofthe integrand on the righthand side of Equation (37) should appear asshown below instead of as in the patent:

Wfi)

same column 10, line 51, the quantity in parentheses in the numerator ofthe righthand side of Equation (.38) should appear as shown belowinstead of as in the patent:

/3 12 22) column 15, line 72, for the system read a system-; column 16,lines 14 to 16, the fraction should appear as shown below instead of asin the patent:

e Signed and sealed this 5th day of July 1960.

[SEAL] Attest: KARL 1-1. AKLINE,

ROBERT C. WATSON, Attestz'ng Oyficer.

aommz'ssioner of Patents.

